This paper concerns with the problem of obtaining non-zero distinct integer solutions to the positive pell equation represented by the binary quadratic equation . A few interesting relations among the solutions are presented. Further, by considering suitable linear combinations among the solutions of the considered hyperbola, the other choices of hyperbolas, parabolas, pythagorian triangle,order Ramanujan numbers, sequence of diophantine 3-tuples with suitable property are presented.

Keywords: Positive pell equation, binary quadratic, hyperbola, parabola, pythagorian triangle, order Ramanujan numbers, sequence of diophantine 3-tuples.